Which decimal is equivalent to 2/7? Choices: (A)0.285714 (B)0.{285714} (C)0.{27} (D)0.27

Calculate Decimal Equivalent: Step 1: Calculate the decimal equivalent of the fraction 2/7 by long division. Divide 2 by 7. The decimal repeats every six digits as 285714.Compare with Choices: Step 2: Compare the calculated decimal with the given choices. The calculated decimal is 0.285714285714..., which repeats the sequence 285714.Identify Correct Choice: Step 3: Identify the correct choice that matches the repeating decimal. Choice (A) is 0.285714, which matches the calculated decimal exactly. Choice (B) is 0.{285714}, which also correctly represents the repeating decimal. Choices (C) and (D) do not match the repeating decimal pattern.

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Which decimal is equivalent to $\frac{2}{7}$ ? $\newline$ Choices: $\newline$ (A) $0.285714$ $\newline$ (B) $0.\overline{285714}$ $\newline$ (C) $0.\overline{27}$ $\newline$ (D) $0.27$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Which decimal is equivalent to

\frac{2}{7}

\newline

Choices:

\newline

(A)

0.285714

\newline

(B)

0.\overline{285714}

\newline

(C)

0.\overline{27}

\newline

(D)

0.27

Calculate Decimal Equivalent: Step $1$ : Calculate the decimal equivalent of the fraction $\frac{2}{7}$ by long division. $\newline$ Divide $2$ by $7$ . The decimal repeats every six digits as $285714$ .
Compare with Choices: Step $2$ : Compare the calculated decimal with the given choices. $\newline$ The calculated decimal is $0.285714285714\ldots$ , which repeats the sequence $285714$ .
Identify Correct Choice: Step $3$ : Identify the correct choice that matches the repeating decimal. Choice (A) is $0.285714$ , which matches the calculated decimal exactly. Choice (B) is $0.\overline{285714}$ , which also correctly represents the repeating decimal. Choices (C) and (D) do not match the repeating decimal pattern.